On the quaternary coding of cubic structures

The notion of a cubant is introduced on the basis of the bijectivity between the set of all n-digital ternary codes and k-dimensional faces of the unit n-cube. The multiplication operation on cubants is defined on the alphabet $\emptyset 0,1,2$. The algebraic structure (monoid) is considered to efficiently determine a number of metric and topological properties of n-dimensional cubic structures. Some perspectives of the proposed methods are discussed with respect to supercomputing.